Image scaling is the process of resizing a digital image which has been widely used in many fields from consumer electronics to medical fields. Scaling is a non-trivial process that involves a tradeoff between efficiency, smoothness and sharpness. In the fields of digital imaging devices, image scaling has a very important role [1], [2]. An important application of image scaling is to scale down the high-quality pictures or video frames to fit to the application such as the mini size liquid crystal display panel of the mobile phone or tablet PC etc.

An image size can be scaled in two ways; up scaling and down scaling. Up scaling is an image enhancement process in which the size of the image is enlarged to fit to the desired application. It is the process of highlighting certain features of interest in an image. Down scaling is the process of image compression which reduces the amount of data needed to represent a digital image. This is done by removing the redundant data from the image. The objective of image compression is to decrease the number of bits required to store and transmit image without any measurable loss of information.

Common interpolation algorithms can be grouped into two categories: adaptive and non-adaptive. Adaptive methods change depending on what they are interpolating (sharp edges vs. smooth texture), whereas non-adaptive methods treat all pixels equally. Non adaptive algorithms include: nearest neighbor, bilinear, bicubic, spline, sinc, lanczos and others. Nearest neighbor algorithm is the simplest method in which the scaled images are full of blocking and aliasing effects. Bilinear interpolation algorithm [3] is the most widely used scaling method, where the target pixel is obtained by the linear interpolation in both horizontal and vertical directions. Another popular non-adaptive method is bicubic interpolation algorithm [4], which is an extension of cubic model. These are some of the polynomial-based methods.

Adaptive algorithms include many proprietary algorithms in licensed software such as: Qimage, PhotoZoom Pro, Genuine Fractals and others. Many non-polynomial-based methods have been proposed in recent years, such as curvature interpolation [5], and autoregressive model [6]. Some previous studies proposed area pixel scaling algorithms such as Winscale [7], edge enhanced scaling algorithm [8] and adaptive edge oriented algorithm [9]. Some of the image scaling processors proposed previously is processor in memory [10], reconfigurable processor [11]. These methods efficiently enhance the image quality also reduce the image artifacts such as blocking, aliasing and blurring effects but these image scaling algorithms are characterized by high complexity and high memory requirement.

DWT is an interpolation technique which is performed with many types of wavelets [12], [13]. Haar wavelet based approach for image compression [14] is an efficient and simplest method for image scaling. Inorder to improve the quality of image than the previous works, DWT with bicubic interpolation is proposed in this work.

Fig. 1. shows the proposed scaling algorithm, which is an area pixel scaling algorithms consisting of a preprocessor, discrete wavelet transform based interpolation, bicubic interpolation and post-processor. Preprocessor converts the original image to gray scale values. To achieve higher visual quality, discrete wavelet transform based interpolation is carried out first and then bicubic interpolation. DWT is based on sub band coding, which divides the image into four frequency quadrants. To reduce the artifacts, bicubic interpolation is carried out to all the four quadrants separately. Bicubic interpolation is an efficient method in which the horizontal and vertical interpolation with nearest 16 pixels is done, which improves the resolution of the image.

Fig. 1

Proposed scaling algorithm

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IIB Pre Processor

Preprocessor converts the original digital image into gray scale values. The discrete levels in a pixel are integers which are assumed to be in the interval [0, L-1] where L is the number of discrete gray levels allowed for each pixel. This should be an integer power of 2.

i.e.,L=2K(1)

View Source{\rm i}.{\rm e}.,\quad {\rm L}=2^{{\rm K}}\eqno{\hbox{(1)}}

The range of values spanned by the gray scale [0, L-1] is called the dynamic range of an image. If the dynamic range is high, then the image will have high contrast and if the dynamic range is low, the image will have a dull, washed out gray look.

IIC Dwt Interpolation

Wavelet transform decomposes a signal into a set of basic functions. These basis functions are called wavelets. Wavelets are obtained from a single prototype wavelet y (t) called mother wavelet by dilations and shifting given by:

ψa,b(t)=1a−−√ψ(t−ba)(2)

View Source\psi_{a, b}(t)={1\over \sqrt{a}}\psi({t-b\over a})\eqno{\hbox{(2)}}

Where a is the scaling parameter and b is the shifting parameter.

In DWT interpolation of image, first the input image is divided into four quadrants according to frequency level. In the second level, each frequency quadrant is divided into sub quadrants and each of these sub quadrants splits according to frequency in the third level. DWT is a technique of decomposition of a complex signal in terms of its mother wavelet and is similar to the expansion of a function in the form of a series. The more the number of terms considered, the higher the accuracy. An image is a two-dimensional signal or a two-variable function. Hence, the series expansion is also two-dimensional. Haar wavelet is one of the oldest, simplest and efficient wavelet used for DWT interpolation.

IIE Post Processor

Post processing converts the interpolated gray scale values to original form and produces the scaled output. The mean square error and peak signal to noise ratio is calculated for the scaled output image To analyze the quality of the scaled image by the scaling algorithm, a peak signal-to-noise ratio (PSNR) is used to quantify a noisy approximation of the refined and the original images. It is the ratio of signal quantity to noise quantity in an image. Since the maximum value of each pixel is 255, the PSNR expressed in dB can be calculated as:

PSNR=10log102552MSE(3)

View SourcePSNR=10log_{10}{255^{2}\over MSE}\eqno{\hbox{(3)}} where, MSE is the mean square error, which is calculated as:

MSE=1mn∑mi=1∑nj=1(xij−yij)2(4)

View Source{\rm MSE} ={1\over {\rm mn}}\sum\nolimits_{{\rm i}=1}^{{\rm m}}\sum\nolimits_{{\rm j}=1}^{{\rm n}}({\rm x}_{{\rm ij}}-{\rm y}_{{\rm ij}})^{2}\eqno{\hbox{(4)}} where m and n are the numbers of rows and columns, respectively. xij and yii denote the original and reconstructed signals, respectively, where i=1:m and j=1:n.

The scaled output image of the proposed method shows that the resulting image is better than the existing bilinear interpolation. To evaluate the performance of the interpolation scheme, Mean Square Error (MSE) and PSNR have been calculated which is expressed in decibel (dB). The average PSNR of the bilinear interpolation is 28.54. In this work PSNR value of different images with three different sizes are verified. From the simulation result, the image “dino” has an average down scaled PSNR of 45.53dB as shown in Table: 1. The down scaled average PSNR values for image crome, flower and dino are 40.49, 42.94 and 45.53 respectively, which are shown in Table: 2., which means that the image quality is improved by a factor of more than 10 dB due of less MSE. The blurring and aliasing effects in the existing method are greatly reduced. Thus, from this simulation result it is clear that the proposed DWT with bicubic interpolation is better in image quality than the existing bilinear method.

Fig. 2

Three sample images in the test set. (a) crome (b) flower (c) dino.

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Table: 1 Down scaled PSNR values of image “dino” with different sizes

Table: 2 Average down scaled PSNR values for three sample images

Fig. 2. lists three sample images in the test set. As an example, the interpolated results of image dino are presented here. Image down scaling is tested and verified for different sizes of the image in this work. The PSNR values for the down scaled image Dino for the sizes 94×94 is 43.36, 117×117 is 45.12 and for 123×123 is 48.13 dB. The simulation results of down scaling and up scaling are shown in Fig. 3. and Fig. 4.

Fig. 3

Down scaled dino result

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The down scaled result of image dino by a factor 0.5 is shown in the Fig. 3., in which, Figure i shows the original image and Figure ii shows the down scaled image. The row and column pixel values of original image are 258 and 774. When it is interpolated, the row and column values changed to 158 and 384 respectively. The PSNR and MSE values of down scaled image dino are obtained as: MSE=2 and PSNR=45.12 dB.

Fig. 4

Up scaled dino result

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The result of up scaling of an image dino by a factor 1.5 is shown in Fig. 4. In the output window, Figure iii shows the original image and Figure iv shows the up scaled image. The row and column pixel values of original image are 258 and 774. When it is interpolated, the corresponding row and column values are scaled to 386 and 1158 respectively. The PSNR and MSE values of up scaled image dino in the proposed method are obtained as: MSE=5428 and PSNR=10.78 dB.

In this approach, a new image scaling algorithm combining the discrete wavelet transform with bicubic interpolation is verified. The sub band coding based fast computation of wavelet transform with simple haar wavelets and reduction of interpolation artifacts of bicubic interpolation gives better image quality. The output image of the simulation shows the reduction of blurring present in existing method. The quality of image is measured by the value of PSNR. The average PSNR values for three different images crome, flower, and dino, when down scaled are obtained as 40.49, 42.94, and 45.53 respectively in this method. Thus the quality of the image is improved by a factor more than 10 dB in this approach, which means that the mean square error is less and gives low visual distortion in the scaled image. Thus this work can achieve better image quality than the existing methods. The simulation of the work is carried out in MATLAB R2013a. The work can be enhanced by using different wavelets in the wavelet family.